Erratum: Differentiability of Relations and Differential Stability of Perturbed Optimization Problems

1988 ◽  
Vol 26 (4) ◽  
pp. 997-998
Author(s):  
Jean-Paul Penot
Keyword(s):  
Optimization Problems ◽  
Differential Stability ◽  
Perturbed Optimization

scholarly journals Differential stability properties in convex scalar and vector optimization

2021 ◽  
Author(s):  
D. T. V. An ◽  
C. Gutiérrez
Keyword(s):  
Optimization Problems ◽  
Lower Semicontinuous ◽  
Scalar Case ◽  
Mathematical Tool ◽  
Optimal Value ◽  
Vector Case ◽  
Differential Stability ◽  
Scalar And Vector Optimization ◽  
Unconstrained Problems ◽  
Semicontinuous Functions

AbstractThis paper focuses on formulas for the ε-subdifferential of the optimal value function of scalar and vector convex optimization problems. These formulas can be applied when the set of solutions of the problem is empty. In the scalar case, both unconstrained problems and problems with an inclusion constraint are considered. For the last ones, limiting results are derived, in such a way that no qualification conditions are required. The main mathematical tool is a limiting calculus rule for the ε-subdifferential of the sum of convex and lower semicontinuous functions defined on a (non necessarily reflexive) Banach space. In the vector case, unconstrained problems are studied and exact formulas are derived by linear scalarizations. These results are based on a concept of infimal set, the notion of cone proper set and an ε-subdifferential for convex vector functions due to Taa.

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